The present invention relates generally to the processes of reprojection-backprojection, and more specifically, to reprojection-backprojection techniques/algorithms that includes new interpolation and data access schemes that result in better speed, lower artifacts. lower noise and higher spatial resolution than existing techniques.
In computed tomography, the operation that transforms an N-Dimension image into an N-Dimension set of line integrals is called the forward projection or reprojection. The most evident example of this operation is the physical process that generates an X-ray image of an object. After logarithmic conversion, an X-ray image is well approximated as the line integral projection of the distribution of the object's linear attenuation coefficient. In practice, a forward projector is required for tomographic simulations or when performing iterative reconstruction.
The transpose operation is called backprojection. This is used in filtered backprojection and in iterative reconstruction, which form the bulk of today's reconstruction algorithms.
Many methods for reprojection and backprojection exist. In one method each X-ray beam is represented by a line and the intersection length of each line with each pixel is used as weight factor. Another technique performs linear interpolation between two pixels for each row or column that the X-ray beam intersects (see FIG. 1). The latter two methods are ray-driven methods.
In the projection case, all projection lines are looped over, and for each projection line the image weighting and summing image pixel values are run through in order to approximate a ray-integral. The backprojection is defined as the transpose operation: the weight factors remain the same, but the detector values are weighted and assigned to the image pixels.
Another technique is the pixel-driven approach, which is typically used in filtered backprojection (see FIG. 2). All image pixels are looped over, and for each image pixel a line is drawn connecting the source and the image pixel. The intersection of that line with the detector array is then determined. Linear interpolation is performed between the two detector values nearest to the intersection point and the result is assigned to the image pixel. The reprojection operation is defined as the transpose operation. The weights for the left and right detector bin are given by
                                                                        ω                l                            =                                                                    d                    r                                    -                  d                                                                      d                    r                                    -                                      d                    l                                                                                                                                          ω                r                            =                                                d                  -                                      d                    l                                                                                        d                    r                                    -                                      d                    l                                                                                                          Eqn        ⁢                                  ⁢                  (          1          )                    where d is the location of the intersection, dr and dl, are the first detector bin centers to the right and to the left of the intersection.
Other approaches exist, such as methods based on spherical basic functions and methods using nearest-neighbor or no interpolation.
The reprojection and backprojection operations are a computationally intensive but essential part of simulation and reconstruction techniques such as those used in CT or the like. Most existing approaches can be subdivided into ray-driven and pixel driven methods. One drawback to both the ray-driven and pixel driven methods resides in the fact that they introduce artifacts, the first one (viz., the ray driven method) in the backprojection and the latter (viz., the pixel driven method) in the reprojection. Another drawback to both methods resides in the percentage of the data used in each view reprojection/backprojection.
For example, in the case of a ray-driven projection of an image with pixels that are much smaller than the detector bin size, only a fraction of the pixels contributes to the projection at that angle. The same is true for the opposite case of the pixel driven backprojection. In iterative reconstruction, where both a reprojection and backprojection method are required, a combination of a ray-driven reprojection and pixel-driven backprojection could be considered to circumvent previous problems. However, even while this is possible, it is often preferred to use a matched reprojector-backprojector pair. In fact, an important criterion in choosing a reprojector-backprojector approach is speed.
The two main limiting factors on speed are arithmetic complexity and data access time. For the ray-driven approach, the arithmetic is relatively simple. It is therefore much faster than the pixel driven approach for small data sizes. At larger data sizes however, the data access time becomes more important and at this stage the pixel-driven approach starts to benefit from its sequential image access time while the ray-driven approach more or less accesses the data randomly. For the 3D cone-beam case, data sets become even larger and therefore data access time gains importance.
For further disclosure pertaining to these techniques and the types of apparatus which are used in connection therewith, reference may be had to U.S. Pat. No. 5,848, 114 issued on Dec. 8, 1998 in the name of Kawai et al.; U.S. Pat. No. 6,351,514 issued in the name of Besson on Feb. 26, 2002; U.S. Pat. No. 6,339,632 issued in the name of Besson on Jan. 15, 2002. The contents of these patents are hereby incorporated by reference thereto.